Lecture 10
Return and Risk
Rates of Return
 A key measure of investors’ success is the
rate at which their funds have grown
 Holding-period return ...
 Return Relative It is a different way to
calculate return. This method is used when a
cumulative wealth index or a geome...
Rates of Return
 Dividend Yield = Percentage return from
dividends i.e. (D/PB)x100
 To calculate HPR over a period of ti...
Arithmetic Average
 It is the sum of periodic return divided by number of
periods
 Arithmetic Average = 15/3 = 5%
Period...
Geometric Average
nth root of the product of returns for n years
Geometric mean = (1+R1)x(1+R2)x(1+R3)1/n
– 1
 = [(1+10%)...
Problem with Arithmetic
average
 Suppose the following:
 Calculating arithmetic mean gives false value of 25% return =
(...
Geometric Vs Arithmetic
 In highly volatile security prices, arithmetic
mean is biased upward and we should use
geometric...
Taking a Global
 When investors buy or sell securities in other
countries, they also take exchange rate risk
or currency ...
An Example
 Suppose you purchased 100 shares of IBM at NYSE for
$300 each. The dollar-rupee parity was 60 rupees a
dollar...
Equation for calculating
returns from foregin stocks
 = [(P1/Po)x(C1/Co)] – 1
 [(310/300)x(78/60)] – 1
 [(1.03) x (1.3)...
Risk
 Any investment involves some degree of
uncertainty about future returns
 Risk arises out of variability in returns...
Type of Risk
Systematic Risk (Not diversifiable)
 Market Risk
 Interest Rate Risk
 Purchasing Power Risk
Unsystematic R...
Sources of Risk
 Market risk : variability in returns due to
fluctuations in aggregate market
 Recession, wars etc
 Int...
 Exchange risk = for international investors,
a source of risk come from exchange rate
fluctuation
 Country Risk = For i...
Interest rates and returns
 1. Increase in interest rates increases the
required rate of return
 RRR= Rf + Risk premium ...
Measuring Risk
 The most commonly used measure of risk
for securities is standard deviation
 SD measure the total risk o...
Standard Deviation
89.5
4
139
15
139
==
−
1
]R-[R
1
2
_
i
−
∑=
n
n
i
Interpretation
 The 5.89 SD means that the security return
can fluctuate between +/-5.89 from the mean
value of 16%
 Mor...
Realized Returns and risk
from Investing
Class of assets Average SD
S&P 500 Composite 9.21% 19.75%
S&P Industrial 9.66 21....
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Risk and Return

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Because of the risk-return tradeoff, you must be aware of your personal risk tolerance when choosing investments for your portfolio. Taking on some risk is the price of achieving returns; therefore, if you want to make money, you can't cut out all risk. The goal instead is to find an appropriate balance - one that generates some profit, but still allows you to sleep at night.

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Risk and Return

  1. 1. Lecture 10 Return and Risk
  2. 2. Rates of Return  A key measure of investors’ success is the rate at which their funds have grown  Holding-period return (HPR) of shares is composed of capital gain and dividend  RH = (C)+ (PE-PB) /PB  This definition assumes end of period returns and ignores re-investment of income
  3. 3.  Return Relative It is a different way to calculate return. This method is used when a cumulative wealth index or a geometric mean has to be calculated. Return Relative (RR)= C+PE/PB Rates of Return
  4. 4. Rates of Return  Dividend Yield = Percentage return from dividends i.e. (D/PB)x100  To calculate HPR over a period of time, we can use:  Arithmetic average  Geometric average  Dollar weighted return
  5. 5. Arithmetic Average  It is the sum of periodic return divided by number of periods  Arithmetic Average = 15/3 = 5% Period 1 10% Period 2 25% Period 3 -20% Sum 15%
  6. 6. Geometric Average nth root of the product of returns for n years Geometric mean = (1+R1)x(1+R2)x(1+R3)1/n – 1  = [(1+10%) x (1+ 25%) x(1+(-20%))] 1/3 – 1  [(1.1) x (1.25) x (.8)] 1/3 – 1  (1.1) 1/3 – 1  1.03-1  .03 or 3%
  7. 7. Problem with Arithmetic average  Suppose the following:  Calculating arithmetic mean gives false value of 25% return = (100%-50%)/2  And geometric = (1+1)x(1-.5)1/2 - 1  =1-1 = 0% Year Begin value Ending value HPR 2007 50 100 100% 2008 100 50 -50%
  8. 8. Geometric Vs Arithmetic  In highly volatile security prices, arithmetic mean is biased upward and we should use geometric mean  If rates of returns are the same for all years, geometric and arithmetic averages gives same results
  9. 9. Taking a Global  When investors buy or sell securities in other countries, they also take exchange rate risk or currency risk  Fluctuation in currency value can be either a source of loss or profit  If the foreign currency strengthens, your returns will increase or vice versa
  10. 10. An Example  Suppose you purchased 100 shares of IBM at NYSE for $300 each. The dollar-rupee parity was 60 rupees a dollar at the that time. So your total investment in rupees was 100x$300 = $30000 x 60 =Rs.1800,000  At the end of the year, IBM share price was $310, giving you $10 profit per share, your profit is = 100 x 10 = $1000x60 = Rs.60000  But the dollar-rupee parity had jumped to 78 rupee a dollar, now your total investment is =100x310 = $31000 x 78 = Rs.2418000  And your profit is 2,418,000-180,0000 = Rs.618,000  Or in percentage = 618,000/1800,000 = .343 or 34%
  11. 11. Equation for calculating returns from foregin stocks  = [(P1/Po)x(C1/Co)] – 1  [(310/300)x(78/60)] – 1  [(1.03) x (1.3)] – 1  1.339 – 1  0.339 or 34%  P1 = Ending share price  Po = Beginning share price  C1 = Ending value of domestic currency  Co = Beginning value of domestic currency
  12. 12. Risk  Any investment involves some degree of uncertainty about future returns  Risk arises out of variability in returns  If an asset has no variability in returns, the assets is considered to be risk free like one year T-bills
  13. 13. Type of Risk Systematic Risk (Not diversifiable)  Market Risk  Interest Rate Risk  Purchasing Power Risk Unsystematic Risks (Diversifiable)  Business Risk  Financial risk
  14. 14. Sources of Risk  Market risk : variability in returns due to fluctuations in aggregate market  Recession, wars etc  Interest Rate Risk Interest risk refers to variability of total returns, particularly on fixed income securities due fluctuation in Interest rates.  Purchas Power or Inflation risk  when purchasing power declines.  Inflation also leads to hike in interest rates because lenders demand more to compensate themselves for loss in purchasing power
  15. 15.  Exchange risk = for international investors, a source of risk come from exchange rate fluctuation  Country Risk = For international investors, economic and political stability, law and order situation are important consideration in the investment decision Sources of Risk
  16. 16. Interest rates and returns  1. Increase in interest rates increases the required rate of return  RRR= Rf + Risk premium which reduces the prices of the securities (intrinsic value)  2. It increases cost of borrowing and hence cost of capital  3. It reduces money supply which lower demand for securities and resultantly prices fall. RRR Cashflow alueIntrinsicV + = 1
  17. 17. Measuring Risk  The most commonly used measure of risk for securities is standard deviation  SD measure the total risk of a security or a portfolio  It measure deviations of each observation from the arithmetic mean 1 ]R-[R 1 2 _ i − = ∑= n n i σ Measuring Risk
  18. 18. Standard Deviation 89.5 4 139 15 139 == − 1 ]R-[R 1 2 _ i − ∑= n n i
  19. 19. Interpretation  The 5.89 SD means that the security return can fluctuate between +/-5.89 from the mean value of 16%  More specifically, the return can fluctuate between 16 - 5.89 = 10.11 or 16 + 5.89 = 21.89 Your return could fall to as low as 10.11% or could rise to 21.89 %
  20. 20. Realized Returns and risk from Investing Class of assets Average SD S&P 500 Composite 9.21% 19.75% S&P Industrial 9.66 21.57 S&P Utility 8.47 20.54 Small Cap Stock (S&P 600) 14.82 37.23 AAA 20-year Corp Bond 3.87 10.05 US 15-year Bond 3.25 10.22 T-Bills 1.569 4.65
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